1) The weakness Galen put in there was not the exhaust port - it was the design of the reactor. The reactor design was unstable, so that any "pressurised explosion" there would set off a chain reaction and destroy the station. The thermal exhaust port was just the way the Rebels found to get that explosion into the core quickly enough.
2) The attack on the DSII did not use a thermal exhaust port. They flew directly into the unfinished structure of the Death Star and flew to the reactor, which they destroyed. It's likely that they used the same design for the weapon of DSII as for DSI, since they didn't have Galen around to come up with a new design.